## Bayes Theorem

The general form of Bayes' theorem (sometimes called Bayes' rule) is:

p(A|X) =-p(X X p( A)-, p(X|A) X p( A) + p(X|~A) X p(~A)

where p(A) is the prior (our prior knowledge, for example, of the prevalence of cancer in the population as a whole);

p(A|X) is the posterior probability (a revised estimate of the probability of A, given X, in our example, of there being cancer, given that the test result was positive);

p(X|A) is the conditional probability of X, given A (in our example, of a positive test when a patient has cancer);

p(X|~A) is the conditional probability of X, given not-A (in our example, of a positive test when a patient does not have cancer).

Same as Bayes'rule. See BayesianMethod.

Bayesian Method 27

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